Hesitant fuzzy sets: State of the art and future directions

International Journal of Intelligent Systems

Volumn 29, Issue 6, 2014, Pages 495-524

  Rodriguez R M ^a   Martinez L ^a   Torra, V ^c   Xu, Z S ^d   Herrera, F ^b,e  

^a UNIVERSITY OF JAÉN   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

^c ARTIFICIAL INTELLIGENCE RESEARCH INSTITUTE IIIA CSIC   (Spain)

^d Department of Management Science and System Science   (China)

^e KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

[No Author keywords available]

Indexed keywords

TOOLS;

ATANASSOV'S INTUITIONISTIC FUZZY SETS; HESITANT FUZZY SETS; INTERVAL-VALUED FUZZY SETS; REAL-WORLD PROBLEM; RESEARCH CHALLENGES; STATE OF THE ART; TYPE-2 FUZZY SET;

FUZZY SETS;

EID: 84898947675     PISSN: 08848173     EISSN: 1098111X     Source Type: Journal    
DOI: 10.1002/int.21654     Document Type: Article

References (73)

1. Nillsson NJ,. Probabilistic logic. Artif Intell 1986; 28: 71-87.
2. Zadeh L,. Fuzzy sets. Inform Control 1965; 8: 338-353.
3. Pawlak Z,. Rough sets. Int J Comput Inform Sci 1982; 11: 341-356.
4. McDermott D, Doyle J,. Non-monotonic logic I. Artif Intell 1980; 13 (1-2): 41-72.
5. Xu Y, Liu J, Martínez L, Ruan D,. Some views on information fusion and logic based approaches in decision making under uncertainty. J Univ Comput Sci 2010; 16 (1): 3-19.
6. Atanassov KT,. Intuitionistic fuzzy sets. Fuzzy Sets and Systems 1986; 20: 87-96.
7. Dubois D, Prade H,. Fundamentals of fuzzy sets, voloume 7 of The handbooks of fuzzy sets. Berlin, Germany: Springer; 2000.
8. Bustince H, Fernandez J, Kolesárová A, Mesiar R,. Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst 2013; 220: 69-77.
9. Türkşen IB,. Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 1986; 20: 191-210.
10. Yager RR,. On the theory of bags. Int J Generation Syst 1986; 13: 23-37.
11. Torra V,. Hesitant fuzzy sets. Int J Intell Syst 2010; 25 (6): 529-539.
12. Chen N, Xu ZS, Xia MM,. Interval-valued hesitant preference relations and their applications to group decision making. Knowl-Based Syst 2013; 37 (1): 528-540.
13. Qian G, Wang H, Feng X,. Generalized hesitant fuzzy sets and their application in decision support system. Knowl-Based Syst 2013; 37 (1): 357-365.
14. Yu D,. Triangular hesitant fuzzy set and its application to teaching quality evaluation. J Inform Comput Sci 2013; 10 (7): 1925-1934.
15. Zhu B, Xu ZS, Xia MM,. Dual hesitant fuzzy sets. J Appl Math 2012; 2012: 1-13.
16. Rodríguez RM, Martínez L, Herrera F,. Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 2012; 20 (1): 109-119.
17. Xia MM, Xu ZS,. Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 2011; 52: 395-407.
18. Bedregal B, Reiser R, Bustince H, Lõpez-Molina C, Torra V,. Aggregating functions for typical hesitant fuzzy elements and the action of automorphisms. Inform Sci 2014; 256 (1): 82-97.
19. Torra V, Narukawa Y,. On hesitant fuzzy sets and decision. In The 18th IEEE Int Conf on Fuzzy Systems, 2009. pp. 1378-1382.
20. Farhadinia B,. A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int J Intell Syst 2013; 28 (8): 752-767.
21. Torra V, Narukawa Y,. Modeling decisions: information fusion and aggregation operators. Springer, 2007.
22. Mesiar R, Mesiarova-Zemankova A,. The ordered modular averages. IEEE Trans Fuzzy Syst 2011; 19 (1): 42-50.
23. Klir GJ, Yuan B,. Fuzzy sets and fuzzy logic: Theory and applications. Singapore: Prentice-Hall PTR; 1995.
24. Herrera F, Alonso S, Chiclana F, Herrera-Viedma E,. Computing with words in decision making: Foundations, trends and prospects. Fuzzy Optim Decis Making 2009; 8 (4): 337-364.
25. Martínez L, Herrera F,. An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Inform Sci 2012; 207 (1): 1-18.
26. Martínez L, Ruan D, Herrera F,. Computing with words in decision support systems: an overview on models and applications. Int J Comput Intell Syst 2010; 3 (4): 382-395.
27. Mendel JM,. An architecture for making judgement using computing with words. Int J Appl Math Comput Sci 2002; 12 (3): 325-335.
28. Rodríguez RM, Martínez L,. An analysis of symbolic linguistic computing models in decision making. Int J Gen Syst 2013; 42 (1): 121-136.
29. Agell N, Sánchez M, Prats F, Rosellõ L,. Ranking multi-attribute alternatives on the basis of linguistic labels in group decisions. Inform Sci 2012; 209 (1): 49-60.
30. Dong Y, Zhang G, Hong WC, Yu S,. Linguistic computational model based on 2-tuples and intervals. IEEE Trans Fuzzy Syst 2013; 21 (6): 1006-1017.
31. Ma J, Ruan D, Xu Y, Zhang G,. A fuzzy-set approach to treat determinacy and consistency of linguistic terms in multi-criteria decision making. Int J Approx Reason 2007; 44 (2): 165-181.
32. Tang Y, Zheng J,. Linguistic modelling based on semantic similarity relation among linguistic labels. Fuzzy Sets Syst 2006; 157 (12): 1662-1673.
33. Wang JH, Hao J,. A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 2006; 14 (3): 435-445. (Pubitemid 43898885)
34. Zadeh L,. The concept of a linguistic variable and its applications to approximate reasoning. Inform Sci 1975; 8: 199-249 (part I), 1975;8:301-357 (part II), 1975;9:43-80 (part III).
35. Rodríguez RM, Martínez L, Herrera F,. A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inform Sci 2013; 241 (1): 28-42.
36. Beg I, Rashid T,. TOPSIS for hesitant fuzzy linguistic term sets. Int J Intell Syst 2013; 28: 1162-1171.
37. Liu H, Rodríguez RM,. A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making. Inform Sci 2014; 258: 266-276.
38. Lee LW, Chen SM,. Fuzzy decision making based on hesitant fuzzy linguistic term sets. In: Intelligent information and database systems, volume 7802 of Lecture Notes in Computer Science, Berlin, Germany: Springer-Verlag; 2013. pp 21-30.
39. Wei C, Zhao N, Tang X,. Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst DOI: 10.1109/TFUZZ.2013.2269144. In press.
40. Zhu B, Xu ZS,. Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst 2014; 22 (1): 35-45.
41. Zhang H, Zheng Q, Liu T, Yang Z, Liu J,. A discrete region-based approach to improve the consistency of pair-wise comparison matrix. In 2013 IEEE Int Conf on Fuzzy Systems, DOI: 10.1109/FUZZ-IEEE.2013.6622447; 2013. pp. 1-7.
42. Zhang Z, Wu C,. Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making. J Intell Fuzzy Syst 2014; 26 (5): 2185-2202.
43. Yu D, Wu Y, Zhou W,. Multi-criteria decision making based on Choquet integral under hesitant fuzzy environment. J Comput Inform Syst 2011; 7 (12): 4506-4513.
44. Wei G,. Hesitant fuzzy prioritized operators and their application. Knowl-Based Syst 2012; 31: 176-182.
45. Yu D, Zhang W, Xu Y,. Group decision making under hesitant fuzzy environment with application to personnel evaluation. Knowl-Based Syst 2013; 52: 1-10.
46. Yu D, Wu Y, Zhou W,. Generalized hesitant fuzzy Bonferroni mean and its application in multi-criteria group decision making. J Inform Comput Sci 2012; 9 (2): 267-274.
47. Zhu B, Xu ZS,. Hesitant fuzzy bonferroni means for multicriteria decision making. J Oper Res Soc 2013; 64 (12): 1831-1840.
48. Zhu B, Xu ZS, Xia MM,. Hesitant fuzzy geometric Bonferroni means. Inform Sci 2012; 205: 72-85.
49. Hardy GH, Littlewood JE, Põlya G,. Inequalities. Cambridge Mathematical Library. Cambridge University Press, 2nd Edition, 1988.
50. Xia MM, Xu ZS, Chen N,. Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decision Negotiation 2013; 22 (2): 259-279.
51. Liu J, Sun M,. Generalized power average operator of hesitant fuzzy numbers and its application in multiple attribute decision making. Journal of Computational Inform Syst 2013; 9 (8): 3051-3058.
52. Zhang Z,. Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Inform Sci 2013; 234: 150-181.
53. Xu ZS, Xia MM,. Distance and similarity measures for hesitant fuzzy sets. Inform Sci 2011; 181 (11): 2128-2138.
54. Xu ZS, Xia MM,. On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 2011; 26 (5): 410-425.
55. Zhou X, Li Q,. Some new similarity measures for hesitant fuzzy sets and their applications in multiple attribute decision making. Comput Res Repository, In press.
56. Fan J, Xie W,. Some notes on similarity measure and proximity measure. Fuzzy Sets Syst 1999; 101 (3): 403-412. (Pubitemid 129505461)
57. Hung WL, Yang MS,. On similarity measures between intuitionistic fuzzy sets. Int J Intell Syst 2008; 23 (3): 364-383.
58. Zeng W, Li H,. Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Sets Syst 2006; 157 (11): 1477-1484.
59. Hung WL, Yang MS,. Similarity measures between type-2 fuzzy sets. International Journal of Uncertainty, Fuzziness Knowl-Based Syst 2004; 12 (6): 827-841.
60. Peng DH, Gao CY, Gao ZF,. Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making. Appl Math Model 2013; 37 (8): 5837-5850.
61. Xu ZS, Chen J,. Ordered weighted distance measure. J Syst Sci Syst Eng 2008; 17 (4): 432-445.
62. Bustince H, Burillo P,. Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 1995; 74 (2): 237-244.
63. Chen N, Xu ZS, Xia MM,. Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 2013; 37 (4): 2197-2211.
64. Zadeh L,. Probability measures of fuzzy events. J Math Anal Appl 1968; 23 (2): 421-427.
65. Xu ZS, Xia MM,. Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision making. Int J Intell Syst 2012; 27 (9): 799-822.
66. Farhadinia B,. Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inform Sci 2013; 240: 129-144.
67. Liao HC, Xu ZS,. A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim Decis Making 2013; 12 (4): 373-392.
68. Xu ZS, Zhang X,. Hesitant fuzzy multi-attribute decision making based on {TOPSIS} with incomplete weight information. Knowledge-Based Systems 2013; 52 (0): 53-64.
69. Zhang N, Wei G,. Extension of VIKOR method for decision making problem based on hesitant fuzzy set. Appl Math Model 2013; 37 (7): 4938-4947.
70. Sahu N, Thakur GS,. Hesitant distance similarity measures for document clustering. In World Congress on Information and Communication Technologies (WICT), Mumbai, India; 2011. pp 430-438.
71. Zhang XL, Xu ZS,. A MST clustering analysis method under hesitant fuzzy environment. Control Cybern 2012; 41 (3): 645-666.
72. Zhang XL, Xu ZS,. Hesitant fuzzy agglomerative hierarchical clustering algorithms. International J Syst Sci DOI: 10.1080/00207721.2013.797037. In press.
73. Bustince H, Herrera F, Montero J, editors. Fuzzy sets and their extensions: representation, aggregation and models, volume 220 of Studies in fuzziness and soft computing. Berlin, Germany: Springer; 2008.